813390400 has 189 divisors, whose sum is σ = 2161920873. Its totient is φ = 301171200.

The previous prime is 813390371. The next prime is 813390407. The reversal of 813390400 is 4093318.

The square root of 813390400 is 28520.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in only one way, i.e., 292820544 + 520569856 = 17112^2 + 22816^2 .

It is not an unprimeable number, because it can be changed into a prime (813390407) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 26238385 + ... + 26238415.

Almost surely, 2^813390400 is an apocalyptic number.

813390400 is a gapful number since it is divisible by the number (80) formed by its first and last digit.

813390400 is the 28520-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 813390400

813390400 is an abundant number, since it is smaller than the sum of its proper divisors (1348530473).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

813390400 is a wasteful number, since it uses less digits than its factorization.

813390400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 130 (or 61 counting only the distinct ones).

The product of its (nonzero) digits is 2592, while the sum is 28.

The cubic root of 813390400 is about 933.4685291684.

The spelling of 813390400 in words is "eight hundred thirteen million, three hundred ninety thousand, four hundred".